Shailaja P. Shanbhag




Teaching of Mathematics, like that of the other subjects taught at the primary school stage, is predominantly textbook based, rather than competency based. Especially for teaching of Mathematics, the conventional approaches seem to be inadequate in terms of the nature of learning experiences provided and their sequencing. There seems to be hardly any theoretical basis to follow a particular approach to teaching of Mathematics. Hence,  if  learning experiences are based on some sound psychological principles of learning and if they take into account the learner characteristics, it must be possible by a majority of children to attain all the competencies that they are required to attain in a particular class. Mathematics as a subject has often been said to be too abstract for some children.  “Any idea, problem, concept or a body of knowledge can be presented in a form that is simple enough for any particular learner to understand it”(Bruner 1966). Hence, the mode of representation of content is to be planned in such a way that the learner is able to master the corresponding competency. Presentation of learning experiences from concrete to semi-abstract to abstract levels may ensure attainment of a competency by every child.


Mastery learning is an appropriate strategy to overcome the limitations of the existing system of instruction at the primary level (Bloom 1968; Block 1971; Guskey and Gates 1986; and Patterson 1993). It  refers to a level of learning that each pupil attains when he / she is able to give at least 80% correct responses on a unit test that has been constructed based on instructional objectives with respect   to that unit. Carroll (1963) explained the concept of mastery theoretically which was transformed into a learning strategy by Bloom (1968). Research efforts since then have been going on for establishing the effectiveness of the strategy and also to modify the strategy for better results.


Mastery Learning Instructional Strategy (MLIS) is a plan, developed explicitly and systematically to ensure that the learner achieves the expected instructional objectives. It starts with concrete experiences involving actions on the part of the learner and proceeds gradually to the abstract experiences. Such a strategy is based on the theory of instruction as propounded by Bruner, for teaching concepts in Mathematics. The advantage of presenting learning experiences on a concrete to abstract continuum is that those learners who possibly operate at the concrete level find the concrete representations of abstract concepts in Mathematics more amenable for conceptualization. Further, the instructional strategy provides optimum time for learning by employing a mastery-learning paradigm, since the outcome expected is the mastery of the competencies in Mathematics. The MLIS provides learning experiences which are appropriate to the level at which a learner can process information. As a result of this, the learners have a high rate of success experience. It is in this background, a Mastery Learning Instructional Strategy based on the “concrete to abstract” learning continuum for attainment of competencies in Mathematics at the primary level was developed and its effectiveness was experimentally tested.



1. To develop a mastery learning instructional strategy (MILS) based on concrete to abstract learning continuum for the attainment of competencies in Mathematics;

2. To validate the instructional strategy in terms of content accuracy and organization; and language comprehensibility;

3. To study the effectiveness of the instructional strategy in terms of mastery of competencies in Mathematics; and learners’ liking towards mathematics.



1. The mastery learning instructional strategy (MLIS) is effective in enabling mastery of competencies in Mathematics;

2. The MLIS is effective in developing a liking towards study of Mathematics;

3. The MLIS and the conventional approach have differential effect on mastery of competencies in Mathematics;

4. The MLIS and the conventional approach have differential effect on students’ liking towards Mathematics.



Independent Variables:

The instructional strategy based on concrete-abstract learning continuum for teaching mathematics;  the level of mastery of pre-requisite competencies; and the home background of the students. 


Dependent Variables:  

Achievement of the minimum levels of learning in Mathematics and students’ liking towards Mathematics.




 The sample of the study consisted of a total of 129 students of standard II from two schools: one experimental and one conventional.  The two groups were matched on the basis of pre-requisite competencies in mathematics comprising of first standard competencies, sex, age, parental education, availability of academic help at home and students liking towards mathematics using c2 test.



A criterion referenced achievement test was developed to measure the pre-requisite competencies of the students in Mathematics. The learners’ liking towards Mathematics was measured on an interview schedule developed for the purpose.



The pre-test-post-test matched group design was employed in this study. MLIS based on concrete to abstract learning continuum for the attainment of competencies in Mathematics of standard II was developed. It  was designed as per the formulations of Benjamin Bloom for a group-based and teacher-paced strategy. The broad areas of second standard Mathematics identified for developing the MLIS were ‘Understanding the whole numbers and numerals’, and ‘Understanding geometrical shapes’. There were a total of 15 competencies under these two areas. The MLIS consisted of concrete, semi-abstract and abstract level activities and games for each competency with formative tests and enrichment activities for ‘masters’ in the first formative test. The MLIS developed was validated in terms of content accuracy and organisation, and language comprehendability. Implementation of MLIS in classroom involved four major steps viz., defining for mastery, planning for mastery, teaching for mastery, and grading for mastery. The implementation took in to account the components of MLIS viz., ‘Orienting students for mastery’, ‘Specification of  instructional objectives’, and ‘Determination of mastery standard’. MLIS was implemented at concrete, semi-abstract and abstract level for all competencies. First formative test was administered after the implementation of MLIS for each competency or for similar competencies. The formative tests developed in the MLIS were also criterion referenced achievement tests and scoring was done following the same procedure as used for scoring the criterion referenced achievement test scores to measure the pre-requisite competencies of the students. Based on the formative test performance, number of masters and non-masters were identified. Non-masters were provided remedial instruction and activities and second formative test was administered. Number of masters and non-masters were identified based on their performance on the second formative test. Non-masters were provided remedial instruction till they mastered the competency.The summative test to measure the competencies considered in the MLIS was administered after implementation of the strategy. Data obtained were analysed using c2 test and   z-test for their significance.


Effectiveness of the MLIS was determined in terms of achievement of competencies in mathematics and learners liking towards mathematics. In the Experimental School, the effectiveness of the strategy was established by finding the number of masters of each of the fifteen competencies considered in the MLIS and number of masters of overall competency (that is who have mastered 12 or more of the individual competencies).  Significance of proportion of masters and significant proportion for each competency were obtained for the first formative test, the second formative test and the summative test. The  proportion of masters in all the competencies and overall competency in the first formative test were more than the expected proportion of 0.70 to be significant at 0.05 level. Obviously, the proportion of masters in all the individual competencies and overall competency in the second formative test and summative test was also more than the expected proportion of 0.70 to be significant at 0.05 level. Hence, MLIS was successful in producing significant proportion of masters at 0.05 level on the first formative test itself in the experimental group.


After arranging data  on a four-point scale from mild and high liking or disliking, the proportions of students with high and mild liking and disliking on pre-test and post-test were calculated. There was a shift from disliking to liking after the implementation of the MLIS. With a view to test the significance of the shift, a ‘z-test’   was conducted. The two levels of  liking and the two levels of disliking were combined to produce a dichotomous data. The two categories were called “liking” and “disliking” for Mathematics. The  z-value (5.40) obtained was significant at 0.01 level. This indicates that the shift observed from disliking to liking towards Mathematics as a result of teaching through the MLIS was significant. The effectiveness of the MLIS was measured by comparing the achievement of competencies of the experimental group students with that of the conventional group students. This was done by finding the significance of difference between proportion of masters of individual and overall competencies in mathematics of experimental group and the control group. It was found  that all the students in  the experimental group had mastered all the individual competencies. All of them were overall masters of the competencies in Mathematics. In the control group, for four individual competencies, the proportion of masters were more than the expected proportion of 0.73 and hence, significant. For all the remaining eleven individual as well as overall competencies, observed proportion of masters were less than the expected proportion of masters and hence, not significant at 0.05 level. Hence,  all students learning through the MLIS had attained cent percent mastery of competencies, whereas conventional approach had produced significant proportion of masters on only four competencies. In experimental group, 98 per cent  showed a liking towards Mathematics, whereas in conventional group only 52 per cent   showed a liking towards Mathematics. The  c2-value (49.77) obtained was significant.


The Mastery Learning Instructional Strategy for teaching Mathematics at standard II was found to be effective in producing significant proportion of masters. There was a significant gain in the students’ liking for mathematics as a result of learning through the mastery learning instructional strategy. A significant difference was found in achievement of competencies in Mathematics between the students taught by the investigator using the MLIS and those taught by the teacher using conventional approach. Significant difference was found between the experimental group students and comparison group students in their liking for Mathematics.



All the pupils taught through the MLIS mastered all competencies in mathematics. Pupils taught through MLIS develop high liking towards Mathematics as  it provides opportunities to play and perform activities as well as the success experiences that they get while learning.



Block, J. (1971) Mastery Learning: Theory and Practice. Holt, Rinehart, & Winston, New York.

Bloom, B. (1968) Learning for mastery. Evaluation Comment 1, 2, 1-5.

Bloom, B. (1971) Mastery Learning. Holt, Rinehart, & Winston, New York

Bruner, J.S.(1966) Towards a Theory of Instruction. Harvard University Press, Cambridge, Mass.

Carroll, J. (1963) A  model for school learning. Teachers College Record 64, 723-733.

Guskey, T. & Gates, S. (1986) Synthesis of research on the effects of Mastery Learning in elementary and secondary classrooms. Educational Leadership 43, 8, 73-80. 

Patterson, W. (1993) Moving toward mastery learning: one school’s approach.  NASSP Bulletin 77, 554, 96-99.